A simplified model for bi-component droplet heating and evaporation

Abstract

A simplified model for bi-component droplet heating and evaporation is developed and applied for the analysis of the observed average droplet temperatures in a monodisperse spray. The model takes into account all key processes, which take place during this heating and evaporation, including the distribution of temperature and diffusion of liquid species inside the droplet and the effects of the non-unity activity coefficient (ideal and non-ideal models). The effects of recirculation in the moving droplets on heat and mass diffusion within them are taken into account using the effective thermal conductivity and the effective diffusivity models. The previously obtained analytical solution of the transient heat conduction equation inside droplets is incorporated in the numerical code alongside the original analytical solution of the species diffusion equation inside droplets. The predicted time evolution of the average temperatures is shown to be reasonably close to the measured one, especially in the case of pure acetone and acetone-rich mixture droplets. It is shown that the temperatures predicted by the simplified model and the earlier reported vortex model are reasonably close. Also, the temperatures predicted by the ideal and non-ideal models differ by not more than several degrees. This can justify the application of the simplified model with the activity coefficient equal to 1 for the interpretation of the time evolution of temperatures measured with errors more than several degrees.\ud \u

Modelling of heating and evaporation of gasoline fuel droplets: A comparative analysis of approximations

“…Our analysis is based on the analytical solutions to the one-dimensional heat conduction and species diffusion equations inside spherically-symmetric droplets implemented in the numerical code [25,28,12].…”

“…The Effective Thermal Conductivity/Effective Diffusivity (ETC/ED) model has been used in our analysis [12,29]. This model takes into account the effect of finite thermal and mass diffusivities alongside the effect of recirculation inside the droplet [12].…”

“…This model takes into account the effect of finite thermal and mass diffusivities alongside the effect of recirculation inside the droplet [12].…”

“…All other thermo-physical properties of the mixture and the vapour diffusion coefficient are calculated as in [12]. The properties of the quasi-components in the quasi-discrete model are the same as discussed in [27].…”

“…The simplest approach to doing this can be based on the application of the Effective Thermal Conductivity (ETC) model [28,29]. Also, in [12,13], which focused on the modelling of heating and evaporation of bi-component droplets, it was demonstrated that the effect of finite diffusivity and recirculation of liquid species cannot be ignored. These effects were taken into account based on the Effective Diffusivity (ED) model.…”